Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
314 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#3633 |
| commutator, socle, prime radical | C23×C17 | C22×C8 |
| Fitting | C17×#95 | C8 |
| cosocle | C22×#3624 | C23 |
| hypercenter | #95 | #3633 |
| hypocenter | C17 | #13105 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 192. C17 | #13105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763912 | 2 |
| C2×#11763903 | 2 |
| #14545854 | 2 |
| #14544576 | 2 |
| #13105 | 17 |